The selection and design of modern high-performance structural engineering materials is driven by optimizing combinations of mechanical properties such as strength, ductility, toughness, elasticity and requirements for predictable and graceful failure in service. (See, e.g., Asby, M. F. Materials Selection in Mechanical Design, Chapter 6, Pergamon, Oxford, 1992). Highly processable bulk metallic glasses (BMGs) are a new class of engineering materials and have attracted significant technological interest. (See, e.g., Peker, A. & Johnson, W. L., Appl. Phys. Lett. 63, 2342-2344 (1993); Johnson, W. L., MRS Bull. 24, 42-56 (1999); Ashby, M. F. & Greer, A. L., Scr. Mater. 54, 321-326 (2006); Salimon, A. I. et al., Mater. Sci. Eng. A 375, 385-388 (2004); and Greer, A. L., Science 267, 1947-1953 (1995), the disclosures of which are incorporated herein by reference.) Although many BMGs exhibit high strength and show substantial fracture toughness, they lack ductility and fail in an apparently brittle manner in unconstrained loading geometries. (See, Rao, X. et at., Mater. Lett. 50, 279-283 (2001), the disclosure of which is incorporated herein by reference.) For instance, some BMGs exhibit significant plastic deformation in compression or bending tests, but all exhibit negligible plasticity (<0.5% strain) in uniaxial tension.
UniaxiaL compression tests are often used to assess the ductility of BMG materials to distinguish them from glassy alloys, which all lack tensile ductility. (See, e.g., Liu, Y. H. et al., Science 315, 1385-1388 (2007); Hofmann, D. C., Duan, G. & Johnson, W. L., Scr. Mater. 54, 1117-1122 (2006); Fan, C. & Inoue, A., Appl. Phys. Lett. 77, 46-48 (2000); Eckert, J. et al., Intermetallics 10, 1183-1190 (2002); He, G., Löser, W. & Eckert, J., Scr. Mater. 48, 1531-1536 (2003); Lee, M. H. et al., Mater. Lett. 58, 3312-3315 (2004); Lee, M. H. et al., Intermetallics 12, 1133-1137 (2004); Das, J. et al., Phys. Rev. Lett. 94, 205501 (2005); Yao, K. F. et al., Appl. Phys. Lett. 88, 122106 (2006); Eckert, J. et at., Intermetallics 14, 876-881 (2006); Chen, M. et al., Phys. Rev. Lett. 96, 245502 (2006); and Lee, S. Y. et al., J. Mater. Res. 22, 538-543 (2007), the disclosures of which are incorporated herein by reference.) Under compression, an operating shear band is subject to a normal stress that closes the band. Variations in local material properties caused, for example, by nanoscale inhomogeneities and frictional forces (due to closing stresses) combine to arrest persistent slip on individual shear bands. Multiple shear bands are sequentially activated, giving rise to global plasticity (˜1-10% strain).
A geometry that better differentiates the ductility is bending. Here, the sample is subject to both compressive and tensile stresses. Shear bands initiate on the tensile surface but are arrested as they propagate towards the neutral stress axis. (See, e.g., Conner, R. D. et al., J. Appi. Phys. 94, 904-911 (2003); and Ravichandran, G. & Molinari, A., Acta Mater. 53, 4087-4095 (2005), the disclosures of which are incorporated herein by reference.) Deformation is stable unless the shear band at the tensile surface evolves to an opening crack. (See, e.g., Conner, R. D. et al., Acta Mater. 52, 2429-2434 (2004), the disclosure of which is incorporated herein by reference.) In bending, plasticity is greatly enhanced when the characteristic dimension RP of a crack tip's ‘plastic zone’ exceeds ˜D/2, where D is sample thickness and RP is a material length scale related to fracture toughness. For a mode I opening crack, it can be expressed as Equation 1 (For discussion see, Myers, M. A. Mechanical Metallurgy: Principles and Applications (Prentice Hall, Englewood Cliffs, N.J., 1984), the disclosure of which is incorporate herein by reference) below:RP(½)(K1C/Y)2  (Eq. 1)
RP varies from ˜1 m up to ˜1 mm on going from relatively brittle to tough BMGs. (See, Lewandowski, J. J., Wang, W. H. & Greer, A. L., Phil. Mag. Lett. 85, 77-87 (2005), the disclosure of which is incorporated herein by reference.) RP is associated with the maximum spatial extension (band length) of shear bands originating at an opening crack tip. For a specific geometry (for example, a mode I opening crack in tension tests), RP is related to a maximum allowable shear offset along the band. In bending, the most ductile BMG reported is Pt57.5Cu14.7Ni5.3P22.5, with RP≈0.5 mm (K1C=83 MPa m1/2). A 4-mm-thick square beam showed 3% plastic bending strain without cracking. (See, Schroers, J. & Johnson, W. L., Phys. Rev. Lett. 93, 255506 (2004), the disclosure of which is incorporated herein by reference.) Despite large bending and compressive ductility, the Pt57.5Cu14.7Ni5.3P22.5 glass has negligible (<0.5%) ductility in uniaxial tensile tests. In tension, the opening stress on the shear bands enhances strain softening and instability, frictional forces are absent, and a propagating shear band lengthens and slips without limit. Cavitation ultimately ensues within the slipping band and an opening failure follows.
Suppression of tensile instability requires a mechanism to limit shear band extension. Bending produces an inherently inhomogeous stress state where a shear band is arrested by the gradient in applied stress, =2Y/D. Stability against crack opening is geometrically ensured when D/2<RP. Under uniaxial tension, applied stress is uniform. By introducing inhomogeneity in elastic or plastic material properties at a microstructural length scale L, ‘microstructural’ stabilization mechanisms become possible. Shear bands initiated in plastically soft regions (with lower Y or lower shear modulus G) can be arrested in surrounding regions of higher yield stress or stiffness. Stabilization requires that L≈RP. This fundamental concept underlies enhancement of ductility and toughening and is similar to that used in the toughening of plastic by inclusion of rubber particles. (See, e.g., Liang, J. Z. & Li, R. K. Y., J. Appl. Polym. Sci. 77, 409-417 (2000), the disclosure of which is incorporated herein by reference).
To overcome brittle failure in tension, BMG-matrix composites have been introduced. BMG matrix compositions have inhomogeneous microstructures incorporated within an amorphous matrix material. These inhomogeneous microstructures, sometimes with isolated dendrites, stabilize the glass against the catastrophic failure associated with unlimited extension of a shear band and results in enhanced global plasticity and more graceful failure. Tensile strengths of ˜1 GPa, tensile ductility of ˜2-3 percent, and an enhanced mode I fracture toughness of K1C≈40 MPa m1/2 were reported. (See, e.g., Hays, C. C., Kim, C. P. & Johnson, W. L., Phys. Rev. Lett. 84, 2901-2904 (2000); and Szuecs, F., Kim, C. P. & Johnson, W. L., Acta Mater. 49, 1507-1513 (2001), the disclosures of which are incorporated herein by reference.) For example, a BMG matrix composite was discovered in La74Al14(Cu,Ni)12 whereby 5% tensile ductility was achieved with 50% volume fraction of soft second phases. (See, e.g., Lee, M. L. et al., Acta Mater. 52, 4121-4131 (2004), the disclosure of which is incorporated herein by reference.) Although the La-based composite exhibited an ultimate tensile strength of only 435 MPa, the alloy demonstrated that the properties of the monolithic metallic glass (La62Al14(Cu,Ni)24) could be greatly improved through the introduction of a soft second phase. Other desirable composite systems are those with lower density (as with Al-containing alloys) or with higher strength (as with Fe-based alloys). However, to this point it has not been possible to introduce these inhomogeneous microstructures in a controlled manner, i.e., to obtain engineered BMG matrix materials. Accordingly, a need exists for a method to design composites BMG materials.